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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Folded normal distribution ： ウィキペディア英語版 Folded normal distribution | cdf_image = | notation = | parameters =    (location)    (scale) | support = | pdf = $\backslash frac\; \}$ + \frac } | cdf = $\backslash frac\backslash left(\backslash mbox\backslash left(\backslash frac\backslash left(\backslash frac\}\; \backslash ,\; e^\; +\; \backslash mu\; \backslash left(1\; -\; 2\backslash ,\backslash Phi(\backslash tfrac)\; \backslash right)$ | median = | mode = | variance = $\backslash sigma\_Y^2\; =\; \backslash mu^2\; +\; \backslash sigma^2\; -\; \backslash mu\_Y^2$ | skewness = | kurtosis = | entropy = | mgf = | char = | fisher = }} The folded normal distribution is a probability distribution related to the normal distribution. Given a normally distributed random variable ''X'' with mean ''μ'' and variance ''σ''2, the random variable ''Y'' = |''X''| has a folded normal distribution. Such a case may be encountered if only the magnitude of some variable is recorded, but not its sign. The distribution is called Folded because probability mass to the left of the ''x'' = 0 is "folded" over by taking the absolute value. In the physics of heat conduction, the folded normal distribution is a fundamental solution of the heat equation on the upper plane (i.e. a heat kernel). The probability density function (PDF) is given by :$f\_Y(x;\backslash mu,\backslash sigma)=$ \frac } + \frac } for ''x''≥0, and 0 everywhere else. It follows that the cumulative distribution function (CDF) is given by: : $$ F_Y(x; \mu, \sigma) = \frac\left(\mbox\left(\frac\left(\frac} \,\, \exp\left(\frac\right) - \mu \, \mbox\left(\frac\right), The variance then is expressed easily in terms of the mean: : $\backslash sigma\_Y^2\; =\; \backslash mu^2\; +\; \backslash sigma^2\; -\; \backslash mu\_Y^2.$ Both the mean (''μ'') and variance (''σ''2) of ''X'' in the original normal distribution can be interpreted as the location and scale parameters of ''Y'' in the folded distribution. ==Differential equations== The PDF of the folded normal distribution can also be defined by the system of differential equations :$\backslash begin$ \sigma^4 f''(x) + 2\sigma^2 x f'(x) + \left(-\mu ^2+\sigma^2+x^2\right) f(x) = 0 \\ f(0) = \sqrt \, \frac \, e^} \\ f'(0) = 0 \end 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Folded normal distribution」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.